Trajectory Planning And Nonlinear Control For Underactuated Cranes: Design, Analysis, And Applications

Cranes, being heavy industrial engineering machines, have been playing extremely important roles in various fields, such as logistics, construction, metallurgy, and manufacturing, among others. The major task for cranes is to transport cargos from their initial positions to desired locations rapidly and accurately, with negligible swing. Presently, most cranes used in practice are manipulated by human operators, which exhibits such drawbacks as low efficiency, poor antiswing performance, incorrect operations, and high risks. Therefore, with the rapid development of control techniques, the problem of automatic antiswing positioning control for cranes has attracted increasingly growing interests from researchers both at home and abroad, becoming a hot research topic within the robotics and control community. However, cranes, which have fewer control inputs than their degrees of freedom(DOFs) to be controlled, are underactuated and usually suffer from various influences like friction forces and external disturbances. In addition,the system state variables are highly, nonlinearly coupled. These factors bring great challenges for the development of antiswing positioning control strategies.To date, though fruitful results have been derived for controlling underactuated cranes, the following drawbacks, from the practical application perspective, are associated with existing methods: 1) most of them overlook the motion(trajectory) planning part and are unable to ensure some practical constraints/indices;2) currently available trajectory planning methods require abundant offline computing/optimizing operations in advance of implementation, and moreover, if the transferring distance changes, it is needed to recalculate the trajectory parameters; 3) most regulation control schemes are sensitive to parametric uncertainties; 4)existing tracking control methods require reference trajectories to satisfy some specific constraints, limiting their practical applicability; 5) most closed-loop schemes require full state feedback and can neither be applicable to three-dimensional(3-D) underactuated cranes nor respect actuator saturation constraints; 6) presentlyavailable controllers designed for varying-rope-length crane systems need to linearize the nonlinear dynamics when developed and/or analyzed, and they cannot ensure the bounds for the tracking errors or be applicable to the case of unknown parameters; 7) neither unmodeled system dynamics nor extraneous disturbances are taken into account when designing and analyzing control laws.Motivated by the desire to tackle the abovementioned problems and drawbacks, this dissertation carries out, from the viewpoint of practical applications,some insightful studies in developing high-performance antiswing positioning control strategies for crane systems. The main contributions are summarized as follows:1) Transportation-oriented trajectory planning for cranes. The payload swing is directly influenced by the trolley acceleration/deceleration motion. By analyzing the trolley/payload kinematic coupling, two trajectory planning methods are presented, which can achieve simultaneous accurate positioning and swing elimination. Specifically, the first method is developed by implementing geometric analysis for the phase plane and it presents three trolley trajectories with analytical expressions. The planned trajectories can guarantee that the maximum swing amplitude and trolley velocity/acceleration to be always within prescribed bounds with no residual swing. The second method is a nonlinear coupling analysis-based online trajectory planning strategy, which can generate smooth swing-free trolley trajectories in real time, without any offline optimization. Extensive simulation and experimental results are exhibited to demonstrate the control performance of these two trajectory planning methods.2) End-effector’s(payload’s) generalized motion-based regulation and tracking control strategies. To overcome the drawbacks associated with the state-of-theart regulation and tracking controllers, this dissertation proposes a novel concept of end-effector’s generalized horizontal motion, and then, the objective of trolley positioning and swing suppression is transformed to the regulation/tracking control problem of the payload’s generalized horizontal motion. Based on this concept, three nonlinear control methods are proposed. The first method yields a model-free regulation controller with a simple structure, which enhances the trol-ley/payload coupling and improves the transient control performance to a great extent. Then the second method gives a new trajectory tracking control law,which relaxes traditional constraints imposed on reference trajectories by existing controllers, achieves closer tracking and faster swing elimination, and broadens the application range. On the basis of the first two methods, the third method puts forward a modified enhanced coupling nonlinear controller, further improving the control system’s robustness. Using numerical simulation and hardware experimental results, we compare the proposed methods with existing ones as a means to show their superior performance.3) Energy analysis-based output feedback(OFB) control strategies. In order to avoid utilizing velocity feedback and improve the robustness with respect to parametric uncertainties, a model-free OFB control law is presented by introducing a virtual spring-block system, which successfully regulates the entire crane system by means of the energy exchanging and dropping principle. The developed controller can achieve satisfactory performance in the presence of unknown parameters and extraneous perturbations. By further incorporating consideration for the actuator saturation constraints, we design a virtual payload-based OFB controller for 3-D cranes to enhance the trolley/payload coupling, which can achieve efficient antiswing positioning control with constrained inputs. Detailed simulation and experimental results are provided to verify the practical performance of these two OFB control strategies.4) Control of cranes in the presence of payload hoisting/lowering. Due to the nonlinear coupling between the state variables, rope length time-variation usually intends to excite severer payload swing. Considering that available methods for varying-rope-length cranes need to simplify the system dynamics and cannot ensure the bounds of the tracking errors, a nonlinear tracking controller is developed, which not only ensures the errors to be always within the preset allowable bounds and then converge to zero, but also relaxes the payload swing range assumption commonly made by existing methods. Subsequently, out of concern for the issue that unknown/uncertain parameters would induce positioning errors in the vertical direction, we then design a new adaptive coupling control law, whichguarantees that the online estimate of the payload mass tends to its true value while achieving accurate trolley/rope length positioning and rapid swing suppression. The proposed adaptive controller yields the first result that successfully addresses the control problem for varying-rope-length cranes subject to parametric uncertainties. In addition to the practical merits mentioned previously, both methods are designed and analyzed without any necessity to approximate the original nonlinear dynamics, and they are hence more general. We use experimental results to validate the proposed methods’ effectiveness and robustness.5) Sliding mode control with consideration for unmodeled dynamics and disturbances. For underactuated crane systems influenced by external disturbances and unmodeled dynamics, a sliding mode-based nonlinear control method is proposed, and it can effectively suppress these perturbations while positioning the trolley to the desired location rapidly and eliminating the payload swing effectively, which is of practical benefit. Additionally, from the theoretical point of view,different from presently available sliding mode control strategies, the proposed method does not require to perform any linearizing or other approximating operations. Moreover, it is shown by experiments that the proposed method achieves better control performance vis-`a-vis several reported methods, in terms of swing suppression, rapid positioning, and robustness.